The 30-year-old Schnyder received a code violation for unsportsmanlike behavior late in the second set for audible obscenities after a prolonged argument with the chair umpire over a line call.
Schnyder, a player's representative for the Australian Open lead up event in Hobart, refused to shake the chair umpire's hand before complaining later about the officiating and the court.
"I didn't expect to play so well today,'' Pironkova said. "I managed to stay in the court and hit deep shots, and she (Schnyder) didn't play her best tennis.
"To beat the (world) No. 14 is a big win, I've only had three or four top-20 wins so this is a big win for me.''
In other matches Sunday, seventh-seeded Alona Bondarenko of Ukraine beat Romanian Monica Niculescu 6-4, 2-6, 6-2, Petra Kvitova of Czech Republic defeated wild card Sally Peers of Australia 6-0, 6-0 and the Czech Republic's Iveta Benesova downed eighth-seeded Tamarine Tanasugarn of Thailand 7-5, 7-5.
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